The Laplace transform of a distribution \({\rho }_{{\rm n}}\)  is called its
moment-generating function (MGF). While the analytic structure of the
Laplace transform is often a source of elegant solution methods and
the reason to use the generating
function [1]}, many problems require only its
formal representation as a power series, and the ensuing linear
algebra. For these, an abstract operator algebra such as that of
Doi [2]}, [3]} is more economical, especially
for evaluating quadratures of Eq. (REF ). The
Doi algebra is reviewed in numerous
places [4]}, [5]}, [6]}, [7]}, [8]},
and we provide only a summary here.
